Mühendislik Fakültesi Koleksiyonu

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https://hdl.handle.net/20.500.14591/11

Now showing 1 - 10 of 10

Priority based vehicle routing for agile blood transportation between donor / client sites
(IEEE, 2017) Karakoç, Mehmet; Günay, Melih
In this paper, we study Vehicle Routing Problem (VRP) for Blood Transporters (BTs) and propose an efficient vehicle routing scheme for blood transportation between hospitals or Donor/Client Sites (DCSs) within a region that is based on Artificial Intelligence. It is assumed that each BT in a fleet of vehicles starts and completes its route at a blood-bank while visiting a subset of DCSs using the shortest path. However, unlike traditional logistic planning, blood transportation may be time critical. Therefore, in our approach, the vehicle routing is formulated to take into account the urgency of the requests and responses. Consequently, the objective of this study is to minimize the number of BTs while maintaining their minimum traveling lengths considering priority. In this regards, we extended the classical Capacitated VRP (CVRP) and reformulated requests to take into account the priority by assigning weight to each request. A hybrid meta-heuristic algorithm including Genetic Algorithms and Local Search is used to simulate transporting blood requests of DCSs. We challenged our approach with symmetrical CVRP instances taken from literature. In this case study, we observed that both the cost and response time are reduced dramatically for emergency.
A new family of Lerch-type zeta functions interpolating a certain class of higher-order Apostol-type numbers and Apostol-type polynomials
(NATL INQUIRY SERVICES CENTRE PTY LTD, 2019) Küçükoğlu, İrem; Şimşek, Yılmaz; Srivastava, H. M.
The aim of this paper is to investigate some classes of higher-order Apostol-type numbers and Apostol-type polynomials. We construct Lerch-type zeta functions which interpolate these numbers and polynomials at negative integers. Moreover, by combining some well-known identities such as the Chu-Vandermonde identity with the Lerch-type zeta functions and generating functions for the higher- order Apostol-type numbers and Apostol-type polynomials, we derive some relations and identities including functional equation for these Lerch-type zeta functions with other zeta type functions, Raabe-type multiplication formula for the higher-order Apostol-type polynomials and the Stirling numbers. Finally, we give some remarks and observations on Lerch-type zeta functions and their functional equations.
Let me make mathematics and music together: A meta-analysis of the causal role of music interventions on mathematics achievement
(ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD, 2023) Akın, Ayça
This research aims to conduct a fixed-effects meta-analysis to unpack the causal role of music interventions on mathematics achievement. Findings indicated that music interventions had a small to moderate positive effect on mathematics achievement (N = 77,595, k = 245, g = 0.36, p < 0.01, 95% CI [0.34, 0.38]). Mathematics skills, instructional mathematical content, types of music interventions, and age were significant moderators, whereas development status was not a significant moderator for this meta-analysis. The most crucial result was that studies using music-mathematics integrated intervention produced a large effect size. This study can be considered interesting in terms of revealing that a significantly strong and positive transfer in mathematics learning was only achieved when used mathematics and music together in the learning environment. Consequently, the current research is regarded to have laid some groundwork for further meta-analytic investigations as it provides detailed, up-to-date, and useful evidence on this issue.
A note on polylogarithms and incomplete gamma function
(UNIV BELGRADE, FAC ELECTRICAL ENGINEERING, 2020) Aygüneş, Aykut Ahmet
In this paper, we firstly introduce the polylogarithms and incomplete gamma function. Then, we claim that there is a relation between polylogarithms and a generalization of incomplete gamma function. Secondly, we give a formula related to polylogarithms. Also,we obtain a relation between incomplete gamma function and the derivatives of polylogarithms. Finally, we find a generating function for the values of incomplete gamma function.
Some approximations with hurwitz zeta function
(UNIV NIS, FAC SCI MATH, 2020) Aygüneş, Aykut Ahmet
In this paper, we focus on some approximations with Hurwitz zeta function. By using these approximations, we present some asymptotic formulae related to Hurwitz zeta function. As an application, we give two corollaries related to Bernoulli polynomials.
Convolution identities for new numbers including Euler and Bernoulli numbers
(AMER INST PHYSICS, 2018) Aygüneş, Aykut Ahmet
In this paper, we firstly give the generating functions of the Bernoulli and Euler polynomials. Secondly. for our main result, we define the generating function of number A(n) in terms of Bernoulli and Euler numbers. Then, we obtain an identity for the Bernoulli and Euler numbers.
Convolution formulae related to special case of Euler and Bernoulli polynomials
(AMER INST PHYSICS, 2019) Aygüneş, Aykut Ahmet
In this paper, we give the generating function of the Euler and Bernoulli polynomials.Then, by using the generating function of these polynomials, we obtain two convolution formulae for some special cases of Euler and Bernoulli polynomials.
Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017) Srivastava, Hari M.; Küçükoğlu, İrem; Şimşek, Yılmaz
The main motivation of this paper is to investigate some derivative properties of the generating functions for the numbers Y-n (lambda) and the polynomials Y-n(x; lambda), which were recently introduced by Simsek [30]. We give functional equations and differential equations (PDEs) of these generating functions. By using these functional and differential equations, we derive not only recurrence relations, but also several other identities and relations for these numbers and polynomials. Our identities include the Apostol Bernoulli numbers, the Apostol Euler numbers, the Stirling numbers of the first kind, the Cauchy numbers and the Hurwitz-Lerch zeta functions. Moreover, we give hypergeometric function representation for an integral involving these numbers and polynomials. Finally, we give infinite series representations of the numbers Y-n (lambda), the Changhee numbers, the Daehee numbers, the Lucas numbers and the Humbert polynomials. (C) 2017 Elsevier Inc. All rights reserved.
On interpolation functions for the number of k-ary Lyndon words associated with the Apostol-Euler numbers and their applications
(SPRINGER-VERLAG ITALIA SRL, 2019) Küçükoğlu, İrem; Şimşek, Yılmaz
The aim of this paper is to construct interpolation functions for the numbers of the k-ary Lyndon words which count n digit primitive necklace class representative on the set of the k-letter alphabet. By using the unified zeta-type function and the unification of the Apostol-type numbers which are defined by Ozden et al. (Comput Math Appl 60:2779-2787, 2010), we give an alternating series for the numbers of the k-ary Lyndon words, in terms of the Apostol-Euler numbers and Frobenius-Euler numbers. We investigate various properties of these functions. Furthermore, applying higher order derivative operator to the interpolation functions for the Lyndon words, we derive ODEs including Stirling-type numbers, the Apostol-Euler numbers, the unified zeta-type functions and also combinatorial sums. By using recurrence relation of the Apostol-Euler numbers, we give computation algorithms for computing not only the Apostol-Euler numbers but also the interpolation functions of the numbers . We also give some remarks, observations and computations for sums of infinite series including these interpolation functions.
k-ary Lyndon words and necklaces arising as rational arguments of Hurwitz-lerch zeta function and Apostol-bernoulli polynomials
(SPRINGER BASEL AG, 2017) Küçükoğlu, İrem; Bayad, Abdelmejid; Şimşek, Yılmaz
The main motivation of this paper was to give finite and infinite generating functions for the numbers of the k-ary Lyndon words and necklaces. In order to construct our new generating functions, we use two different methods. The first method is related to the derivative operator t d/dt and the Stirling numbers of the second kind. On the other hand, the second method is related to the Hurwitz-Lerch zeta function and the Apostol-Bernoulli numbers. Moreover, by using these generating functions, we give some applications for some selected numerical values including different prime numbers factorization, the Stirling numbers and also the Bernoulli numbers and polynomials.

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